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• National Health Surveys
• Public Health Research
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NHMS Reports

https://iku.nih.gov.my/nhms

The Sampling Problem

The Sampling Problem

• In describing a population, we often use a handful of samples rather than the whole population.
• Unfortunately, sample distribution may differ from the population - gender, ethnicity, age.
• Small studies typically limit their sample; clearly define the target population using inclusive and exclusive criteria.
• But national surveys, including health surveys, require the sample to represent the general population (e.g., adult population, older person population, maternal and child population).

Malaysian Population, 2025

• This is the Malaysian population pyramid.
• Source: Open DOSM Data Dashboard

The codes

pacman::p_load(tidyverse, arrow)

pyr_df <- read_parquet("https://storage.dosm.gov.my/population/population_malaysia.parquet") %>%
  filter(date == as.Date("2025-01-01"), sex %in% c("male", "female"), 
         age != "overall", ethnicity == "overall") %>%
  mutate(pop_k = population, pop = if_else(sex == "male", -pop_k, pop_k), 
         age0 = readr::parse_number(age), age = fct_reorder(age, age0))

my_pyr_plot <- ggplot(pyr_df, aes(x = age, y = pop, fill = sex)) + 
  geom_col(width = 0.9) + coord_flip() +
  scale_y_continuous(limits = c(-2000, 2000), breaks = seq(-2000, 2000, 500), 
                     labels = function(x) scales::comma(abs(x)), 
                     expand = expansion(mult = c(0.02, 0.02))) +
  labs(title = "Malaysia Population Pyramid, 2025", x = "Age group (years)", 
       y = "Population (thousands)", fill = "Sex") +
  theme_minimal(base_size = 13) + theme(panel.grid.minor = element_blank())

my_pyr_plot

Why Complex Sampling?

• Sampling: We use a sample to estimate the population efficiently, saving time, cost, and resources while still capturing key characteristics.
• Stratification: Stratifying (by gender, ethnicity) ensures all important subgroups are represented and improves precision of estimates.
• Clustering: Clustering respondents by area makes data collection logistically practical and cost-efficient.

What is Complex Sampling?

• Structured selection – Instead of simple random sampling, respondents are chosen through stratified and clustered sampling to ensure representation across diverse groups.
• Unequal probabilities – Some groups are oversampled (e.g., small states, older adults) to obtain reliable estimates, necessitating the use of sampling weights to correct for these differences.
• Design-based inference – Analysis must account for the survey’s design, including strata, clusters, and weights,so that standard errors and prevalence estimates accurately reflect the true population.

Example (NHMS 2023) – Diabetes Prevalence

Simulation

• We try to mimic typical survey at field.
  • 1,100 synthetic respondents.
  • Age groups: 18–29 to 60+.
  • Sex ratio 40 % male / 60 % female.
  • Ethnicity: 65 % Malay, 20 % Chinese, 15 % Indian.
  • Out of 1,100 respondents, 242 have DM
• The simulated dataset is available on GitHub: https://github.com/MohdAzmiSuliman/MyRUG_ComplexSamplingNHMS

The codes

tibble(age_group = c("18-29","30-39","40-49","50-59","60+"), n_total = c(200, 200, 200, 200, 300)) %>% 
  mutate(male = as.integer(round(.4*n_total)), female = n_total - male) %>% 
  pivot_longer(male:female, names_to = "gender", values_to = "n_gender") %>% 
  mutate(malay = as.integer(round(.65*n_gender)), chinese = as.integer(round(.2*n_gender)), 
         indian = n_gender - malay - chinese) %>% 
  pivot_longer(malay:indian, names_to = "ethnicity", values_to = "n_ethnic") %>% 
  uncount(n_ethnic) %>% select(-starts_with("n_")) %>% group_by(age_group) %>% 
  mutate(age = case_when(age_group == "18-29" ~ sample(18:29, n(), replace = T), 
                         age_group == "30-39" ~ sample(30:39, n(), replace = T), 
                         age_group == "40-49" ~ sample(40:49, n(), replace = T), 
                         age_group == "50-59" ~ sample(50:59, n(), replace = T), 
                         .default = sample(60:90, n(), replace = T))) %>% ungroup() %>% 
  mutate(dm = c(rep(0, 50), rep(1, 2), rep(0, 15), rep(1, 1), rep(0, 11), rep(1, 1), rep(0, 76), 
                rep(1, 2), rep(0, 23), rep(1, 1), rep(0, 17), rep(1, 1), rep(0, 48), rep(1, 4), rep(0, 15), 
                rep(1, 1), rep(0, 11), rep(1, 1), rep(0, 73), rep(1, 5), rep(0, 23), rep(1, 1), rep(0, 16), 
                rep(1, 2), rep(0, 45), rep(1, 7), rep(0, 14), rep(1, 2), rep(0, 9), rep(1, 3), rep(0, 65), 
                rep(1, 13), rep(0, 20), rep(1, 4), rep(0, 13), rep(1, 5), rep(0, 37), rep(1, 15), 
                rep(0, 12), rep(1, 4), rep(0, 6), rep(1, 6), rep(0, 55), rep(1, 23), rep(0, 18), 
                rep(1, 6), rep(0, 9), rep(1, 9), rep(0, 49), rep(1, 29), rep(0, 16), rep(1, 8), rep(0, 7), 
                rep(1, 11), rep(0, 72), rep(1, 45), rep(0, 23), rep(1, 13), rep(0, 10), rep(1, 17)), 
         adw = 20) # adjusted design weight = 20, assume dw = 20 and RR = 100% for all

Crude Proportion

• In epidemiology, prevalence refers to the proportion of a population that has a specific condition at a given time.
• Here, it reflects the proportion of individuals with diabetes mellitus (DM) in our simulated data.
• We know that 242 out of 1,100 respondents have DM — so the crude prevalence should be 22.0%, right?

Respondent vs Target Population

• But those our respondent actually reflect our target population?
• Let look back at our Malaysian population distribution

Respondent vs Target Population

• But do our respondents actually reflect our target population?
• Let look back at our Malaysian population distribution

Respondent vs Target Population

• But do our respondents actually reflect our target population?
• These  our simulated respondents.

Respondent vs Target Population

• Compared with the Malaysian population, our simulated respondents show:
  • A larger proportion of older adults
  • More females than males

The Calibration - Post-stratification

• To match sample structure to true population totals.
  
• Ensures estimates represent Malaysia accurately.

The Calibration - Post-stratification

• Aligns weights by age, sex, ethnicity.
  
• Focuses on respondent count, national population by strata, and adjustment factor.

Post-Strat Effect – Age

• Younger adults up-weighted → weight ↑.
  
• Older adults down-weighted → weight ↓.

Post-Strat Effect – Gender

• Males under-sampled → weight ↑.
  
• Females over-sampled → weight ↓.

Before and After Weighting

• Weighting restores population structure.

Before and After Weighting

• Weighting restores population structure.

Corrected Prevalence